Aarex's Array Notation or AAN is an array notation created by Aarex Tiaokhiao.[1] The notation is currently composed of the following parts:

  1. Simple Array Notation (sAAN)
  2. Extended Array Notation (exAAN)

Simple Array Notation

Simple Array Notation (sAAN) is the first extension of AAN.

Definition

Expressions in sAAN are of the form a(A), where A is a sequence of non-negative integers separated by commas. The first entry is called the base and the second entry is called the co-base. The # sign is used to represent the rest of the expressions. New copies of old # remain the same.

Main rules

a(a,b,0) = ab

a(#,0)[1] = a(#)

a(a,b,c,#)[1] = a(a,b,c,#)

a(a,b,c,#)[d] = a(a,a(a,b,c,#)[d-1],c,#)

a(a,b,c,#) = a(a,b,c-1,#)[d]

Process rules

If none of the main rules apply, begin at the fourth entry.

Case A: If the entry is 0, move to the next entry.

Case B: Else, decrease the entry by 1 and change the previous entry to the co-base. The process ends.

Issues

The notation is still ill-defined because there is no possible rule to apply to a(1,0,1). Additionally, rule 5 has a "d" that is ill-defined.

Sources

  1. Aarex, Aarex's Array Notation, Google site.
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